Question

43. A rectangle of length 200 m and 100 m width has a path of width 5 m all
along the inside boundary. What is the area of that path?
(a) 2,900 m² (b) 2,500 m² (c) 2,300 m² (d) 2,100 m2​

Answer 1

Given : A rectangle of length 200 m and 100 m width has a path of width 5 m all along the inside boundary.

Exigency to find : The Area of Path .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Finding Area of Rectangle :

⠀⠀⠀⠀⠀$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Area _{(Rectangle)} \:: l \times b }\bigg\rgroup$

⠀⠀⠀⠀⠀Here l is the Length of Rectangle & b is the Breadth of Rectangle .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Area \:= 200 \times 100$

$\qquad \longmapsto \frak{\underline{\purple{\:Area_{(Rectangle)} = 20,000 \:m^2 \:}} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Area \:of\:Rectangle \:is\:\bf{ 20,000\:m^2\:.}}}}$

Now , Given that ,

⠀⠀⠀⠀⠀━━There is a path of width 5 m all along the inside boundary.

Therefore ,

• Length of Rectangle excluding Path : 200 - ( 5+ 5 )

⠀⠀⠀⠀⠀200 - 10

⠀⠀⠀⠀=⠀190 m

• Breadth of Rectangle excluding path : 100 - (5 + 5)

⠀⠀⠀⠀⠀100 - 10

⠀⠀⠀=⠀90 m

Now ,

• Finding Area of Rectangle excluding path to find Area of path :

$\qquad:\implies \sf Area \:= 190 \times 90$

$\qquad \longmapsto \frak{\underline{\purple{\:Area_{(Excluding \:Path\:)}= 17,100 \:m^2 \:}} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Area \:of\:Rectangle\:excluding \:path\:is\:\bf{ 17,100\:m^2\:.}}}}$

⠀⠀⠀⠀⠀Finding Area of Path :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Area _{(Path)} \:: Area_{(Rectangle)} - Area_{(Rectangle\:Excluding\:Path\:)}}\bigg\rgroup$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Area_{(Path)} \:= 20,000 - 17,100$

$\qquad \longmapsto \frak{\underline{\purple{\:Area_{(Path)} = 2,900 \:m^2 \:}} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Area \:of\:\:path\:is\:\bf{ 2,900\:m^2\:.}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

Answer:

2900



Step-by-step explanation: